A 132 kg crate is sitting at the top of a ramp, which is inclined at an angle of 20 degrees with respect to the horizontal. Someone gives the crate a quick shove to get it moving, after which it slides down the ramp without any further assistance. The coefficient of kinetic friction between the crate and the ramp is Hs = 0.24. What is the magnitude of the acceleration (in m/s²) of the crate?

Principles of Physics: A Calculus-Based Text
5th Edition
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Raymond A. Serway, John W. Jewett
Chapter5: More Applications Of Newton’s Laws
Section: Chapter Questions
Problem 61P
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A 132 kg crate is sitting at the top of a ramp, which is inclined at an angle of 20 degrees with
respect to the horizontal. Someone gives the crate a quick shove to get it moving, after which it
slides down the ramp without any further assistance. The coefficient of kinetic friction between the
crate and the ramp is µs = 0.24. What is the magnitude of the acceleration (in m/s²) of the crate?
Transcribed Image Text:A 132 kg crate is sitting at the top of a ramp, which is inclined at an angle of 20 degrees with respect to the horizontal. Someone gives the crate a quick shove to get it moving, after which it slides down the ramp without any further assistance. The coefficient of kinetic friction between the crate and the ramp is µs = 0.24. What is the magnitude of the acceleration (in m/s²) of the crate?
Expert Solution
Step 1

Given:

The mass of the crate is m=132 kg.

The angle is θ=20°.

The coefficient of kinetic friction is μs=0.24.

Let F is the force on the crate.

The expression for acceleration (a) is:

a=Fma=mgsinθ-μmgcosθma=gsinθ-μcosθ

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